Gap created after Screw modifier
There can be gaps but they're not inevitable. 


The Angle should be 360° so the edges line up.
The Screw value should be exactly the same value as the object's dimension in the relevant axis.
The highest and the lowest vert should have the same distance from the screw axis.
After applying the modifier, using Remove Doubles with the relevant verts selected and a large enough threshold should kill any small gaps. Without that, a Subsurf Modifier might produce a gap.